# Malicious Experts versus the multiplicative weights algorithm in online prediction

arXiv: https://arxiv.org/abs/2003.08457 · HTML: https://mlsanity.com/paper/2003.08457/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2020.

## Built on by (most cited first, 6 of 6)

- [PDE-Based Optimal Strategy for Unconstrained Online Learning](https://mlsanity.com/paper/2201.07877/) (2022)
- [Numerical solution of a PDE arising from prediction with expert advice](https://mlsanity.com/paper/2406.05754/) (2024)
- [An explicit solution of the five-expert prediction PDE and the exact optimality set of COMB](https://mlsanity.com/paper/2609.14892/) (2026)
- [A PDE approach for regret bounds under partial monitoring](https://mlsanity.com/paper/2209.01256/) (2022)
- [Reasoning without Regret](https://mlsanity.com/paper/2504.09777/) (2025)
- [On prediction from expert advice with more than five experts](https://mlsanity.com/paper/2610.05186/) (2026)

## Abstract (arXiv)

We consider a prediction problem with two experts and a forecaster. We assume that one of the experts is honest and makes correct prediction with probability μ at each round. The other one is malicious, who knows true outcomes at each round and makes predictions in order to maximize the loss of the forecaster. Assuming the forecaster adopts the classical multiplicative weights algorithm, we find upper and lower bounds for the value function of the malicious expert. Our results imply that the multiplicative weights algorithm cannot resist the corruption of malicious experts. We also show that an adaptive multiplicative weights algorithm is asymptotically optimal for the forecaster, and hence more resistant to the corruption of malicious experts.